The backward shift on spaces of analytic functions

解析函数空间的后移

• 批准号: 0098214
• 负责人: William Ross
• 金额: $ 7.55万
• 依托单位: University of Richmond
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-01 至 2004-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0098214&HistoricalAwards=false
• 关键词: backward; shift; spaces; analytic; functions

In this project, the PI plans to investigate the `continuation' properties of the invariant subspaces of the backward shift operator on various spaces of analytic functions on the unit disk. In 1970, Douglas, Shapiro, and Shields showed that functions belonging to these invariant subspaces of the Hardy space posses special continuation properties to the exterior disk. In more recent investigations, this idea of `continuation' has been shown to be ubiquitous in that it appears to take place, in one form or another, in many other settings belong the Hardy space case. This proposal plans to get at the heart of the nature of these continuations and why they occur in the first place. This project falls under the broad heading of the field of mathematical analysis which, besides its beauty and elegance, makes many connections and has its roots in problems connected with physics and engineering. In fact, the concept of `continuation' properties of analytic functions has been recently studied by the engineer S. Darlington who connected these `continuations' to properties of electrical circuit design.

在这个项目中，PI计划在单位圆盘上的解析函数的各种空间上研究倒移算子的不变子空间的“延拓”性质。1970年，Douglas, Shapiro， and Shields证明了属于Hardy空间的这些不变子空间的函数对外盘具有特殊的延拓性质。在最近的研究中，“延续”的概念被证明是无处不在的，因为它似乎以一种或另一种形式发生，在许多属于哈代空间情况的其他设置中。这一提议计划抓住这些延续的本质的核心，以及它们最初发生的原因。这个项目属于数学分析领域的广泛标题，除了它的美丽和优雅之外，它还与物理和工程相关的问题有许多联系和根源。事实上，解析函数的“延拓”性质的概念最近已经被工程师S. Darlington研究过，他将这些“延拓”与电路设计的性质联系起来。